Question

sides of a Trapezium are 25 cm and 11cm while non parallel sides are 15 cm and 13 cm find the area of trapezium​

Answer 1

Draw CE such that AECD is a parallelogram

AE = CD = 11 cm

AD = CE = 15 cm

EB = 14 cm

Area of ΔECB = \sqrt{s(s-a)(s-b)(s-c)}

s(s−a)(s−b)(s−c)

where s = (a+b+c)/2

a = 13 cm, b = 14 cm, c = 15 cm

Here s = (13+14+15)/2 = 21 cm

Area of ΔECB = \sqrt{21(21-13)(21-14)(21-15)}

21(21−13)(21−14)(21−15)

= \sqrt{21(8)(7)(6)}

21(8)(7)(6)

= 84 sq cm

But Area of ΔECB = 1/2 × base (EB) × height (h)

1/2 × 14 × h = 84

h = 12 cm

Area of trapezium ABCD = 1/2 × h × (AB + CD)

= 1/2 × 12 × (25 + 11)

= 6 × 36

= 216 sq cm